MATH48062 - 2007/2008

 

Specification

Aims

To familiarise students with the ideas and methodology of certain multivariate methods together with their application in data analysis using the S-Plus statistical computing package.

Brief Description of the unit

In practice most sets of data are multivariate in that they consist of observations on several different variables for each of a number of individuals or objects. Indeed, such data sets arise in many areas of science, the social sciences and medicine and techniques for their analysis form an important area of statistics. This course unit introduces a number of techniques, some of which are generalisation of univariate methods, while others are completely new (e.g. principal component analysis). It contains a number of additional topics to those in the third level course unit.

Learning Outcomes

On successful completion of this course unit students will

• be familiar with multivariate random vectors and their probability distributions;
• have acquired skills in dimensionality reduction techniques, inferential methods based on the multivariate Normal distribution as an underlying model and in methods of data classification;
• be able to use S-Plus as a tool for multivariate data analysis and graphical presentation.

Future topics requiring this course unit

This course unit forms a useful background to other statistics course units.

Syllabus

1. Introductory ideas and basic concepts, including simple graphical techniques.
2. Cluster Analysis.
3. Dimensionality reduction: Techniques based on the singular value decomposition of a data matrix - principal component analysis, biplots.
4. The Multivariate Normal (MVN) distribution: Definition. Properties. Conditional distributions. The Wishart and Hotelling T-squared distributions. Maximum likelihood estimation of the mean vector and covariance matrix.
5. Hypothesis testing and confidence intervals (1 and 2 sample procedures).
6. Multivariate Analysis of Variance.
7. Discriminant Analysis.

Textbooks

• Chatfield, C. and Collins, A. J., An Introduction to Multivariate Analysis, Chapman & Hall 1983.
• Krzanowski, W. J., Principles of Multivariate Analysis: A User's Perspective, Oxford University Press 1990.
• Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis 3rd edition, Prentice Hall 1992.

Teaching and learning methods

Three lectures and one examples class each week. In addition students should expect to spend at least six hours each week on private study for this course unit.

Assessment

Coursework: weighting 20%

End of semester examination: two hours weighting 80%

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Arrangements